Search results for "equation"
showing 10 items of 4219 documents
On the hyperporous non-linear elasticity model for fusion-relevant pebble beds
2010
Abstract Packed pebble beds are particular granular systems composed of a large amount of small particles, arranged in irregular lattices and surrounded by a gas filling interstitial spaces. Due to their heterogeneous structure, pebble beds have non-linear and strongly coupled thermal and mechanical behaviours whose constitutive models seem limited, being not suitable for fusion-relevant design-oriented applications. Within the framework of the modelling activities promoted for the lithiated ceramics and beryllium pebble beds foreseen in the Helium-Cooled Pebble Bed breeding blanket concept of DEMO, at the Department of Nuclear Engineering of the University of Palermo (DIN) a thermo-mechani…
Characterization of theTiSiO4structure and its pressure-induced phase transformations: Density functional theory study
2009
Theoretical investigations concerning the possible titanium silicate polymorphs have been performed using density functional theory at B3LYP level. Total-energy calculations and geometry optimizations have been carried out for all phases involved. The following sequence of pressure-driven structural transitions has been found: ${\text{CrVO}}_{4}$-type, $Cmcm$ (in parenthesis the transition pressure), $\ensuremath{\rightarrow}$ zircon-type, $I{4}_{1}/amd$ (0.8 GPa), $\ensuremath{\rightarrow}$ scheelite-type, $I{4}_{1}/a$ (3.8 GPa). At higher pressure the last phase is found to be stable at least up to 25 GPa. The equation of state of the different polymorphs is also reported. We found that t…
High-pressure x-ray diffraction andab initiostudy ofNi2Mo3N,Pd2Mo3N,Pt2Mo3N,Co3Mo3N, andFe3Mo3N: Two families of ultra-incompressible bimetallic inte…
2010
We have studied by means of high-pressure x-ray diffraction the structural stability of ${\text{Ni}}_{2}{\text{Mo}}_{3}\text{N}$, ${\text{Co}}_{3}{\text{Mo}}_{3}\text{N}$, and ${\text{Fe}}_{3}{\text{Mo}}_{3}\text{N}$. We also report ab initio computing modeling of the high-pressure properties of these compounds, ${\text{Pd}}_{2}{\text{Mo}}_{3}\text{N}$ and ${\text{Pt}}_{2}{\text{Mo}}_{3}\text{N}$. We have found that the nitrides remain stable in the ambient-pressure cubic structure at least up to 50 GPa and determined their equation of state. All of them have a bulk modulus larger than 300 GPa. Single-crystal elastic constants have been calculated in order to quantify the stiffness of the i…
Theoretical study of a Bénard Marangoni problem
2011
[EN] In this paper we prove the existence of strong solutions for the stationary Benard-Marangoni problem in a finite domain flat on the top, bifurcating from the basic heat conductive state. The Benard-Marangoni problem is a physical phenomenon of thermal convection in which the effects of buoyancy and surface tension are taken into account. This problem is modelled with a system of partial differential equations of the type Navier-Stokes and heat equation. The boundary conditions include crossed boundary conditions involving tangential derivatives of the temperature and normal derivatives of the velocity field. To define tangential derivatives at the boundary, intended in the trace sense,…
A COMPARATIVE STUDY BETWEEN ´ BIHARMONIC BEZIER SURFACES AND BIHARMONIC EXTREMAL SURFACES
2009
AbstractGiven a prescribed boundary of a Bezier surface, we compare the Bezier surfaces generated by two different methods, i.e., the Bezier surface minimising the biharmonic functional and the unique Bezier surface solution of the biharmonic equation with prescribed boundary. Although often the two types of surfaces look visually the same, we show that they are indeed different. In this paper, we provide a theoretical argument showing why the two types of surfaces are not always the same.
Two -methods to generate Bézier surfaces from the boundary
2009
Two methods to generate tensor-product Bezier surface patches from their boundary curves and with tangent conditions along them are presented. The first one is based on the tetraharmonic equation: we show the existence and uniqueness of the solution of @D^4x->=0 with prescribed boundary and adjacent to the boundary control points of a nxn Bezier surface. The second one is based on the nonhomogeneous biharmonic equation @D^2x->=p, where p could be understood as a vectorial load adapted to the C^1-boundary conditions.
PDE triangular Bézier surfaces: Harmonic, biharmonic and isotropic surfaces
2011
We approach surface design by solving second-order and fourth-order Partial Differential Equations (PDEs). We present many methods for designing triangular Bézier PDE surfaces given different sets of prescribed control points and including the special cases of harmonic and biharmonic surfaces. Moreover, we introduce and study a second-order and a fourth-order symmetric operator to overcome the anisotropy drawback of the harmonic and biharmonic operators over triangular Bézier surfaces. © 2010 Elsevier B.V. All rights reserved.
A third order partial differential equation for isotropic boundary based triangular Bézier surface generation
2011
Abstract We approach surface design by solving a linear third order Partial Differential Equation (PDE). We present an explicit polynomial solution method for triangular Bezier PDE surface generation characterized by a boundary configuration. The third order PDE comes from a symmetric operator defined here to overcome the anisotropy drawback of any operator over triangular Bezier surfaces.
Explicit Bézier control net of a PDE surface
2017
The PDE under study here is a general fourth-order linear elliptic Partial Differential Equation. Having prescribed the boundary control points, we provide the explicit expression of the whole control net of the associated PDE Bézier surface. In other words, we obtain the explicit expressions of the interior control points as linear combinations of free boundary control points. The set of scalar coefficients of these combinations works like a mould for PDE surfaces. Thus, once this mould has been computed for a given degree, real-time manipulation of the resulting surfaces becomes possible by modifying the prescribed information. The work was partially supported by Spanish Ministry of Econo…
Effect of stiffness on the phase behavior of cubic lattice chains
2005
Gran canonica Monte Carlo (GCMC) simulazioni assistite da tecniche di riponderazione istogramma sono stati utilizzati per studiare l'effetto della flessibilità catena sul comportamento di soluzione fase di cubi catene reticolari corti con 4-32 segmenti. Ciò è stato fatto variando un parametro di rigidità gradualmente fino alla media calcolata end-to-end distanza avvicinato la lunghezza totale. Per entrambe le catene flessibili e rigide si è riscontrato che la temperatura critica, ottenuta tramite mista analisi dei campi di dimensioni finite, aumentata lunghezza della catena e la densità critica trasferisce a valori più bassi, in accordo con le osservazioni sperimentali. Il estrapolato lungh…